Question

If the common difference of an ap is 3 then a20 - a15 is

Answer 1

Answer:

We know that,

an=a+(n-1)d

So,a20=a+(20-1)(3)

a20=a+19(3)

a20=a+57

Similarly, a15=a+14d

a15=a+14(3)

a15=a+42

Now,a20-a15=(a+57)-(a+42)

=a+57-a-42

=57-42

=15

Answer 2

GIVEN :–

• Common difference (d) = 3

TO FIND :–

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• $\bf a_{20} - a_{15} = ?$

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SOLUTION :–

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• We know that nth term of A.P. if first term is 'a' –

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$\bf \implies \large{ \boxed{ \bf a_{n} = a + (n - 1)d }}$

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• Now –

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$\bf \implies a_{20} = a + (20 - 1)d$

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$\bf \implies a_{20} = a +19d$

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• And –

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$\bf \implies a_{15} = a + (15 - 1)d$

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$\bf \implies a_{15} = a +14d$

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• So that –

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$\bf \implies a_{20} - a_{15} =(a +19d) - (a + 14d)$

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$\bf \implies a_{20} - a_{15} = 19d- 14d$

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$\bf \implies a_{20} - a_{15} = 5d$

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$\bf \implies a_{20} - a_{15} = 5(3)$

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$\bf \implies \large{ \boxed{ \bf a_{20} - a_{15} = 15}}$